How to use
- Paste two columns, one person per row. A header row is optional.
- For a one-sided test, pick "first column is larger" or "smaller".
- Read the p-value and the median difference (first column minus second).
- Copy the APA line for your report.
Options explained
- W+ and W−
- The absolute differences are ranked; W+ is the sum of ranks of positive differences and W− of negative ones. R reports W+ (as V); SPSS and many textbooks report the smaller of the two.
- Zero differences
- Pairs with a difference of 0 are dropped, as R does by default. The result tells you how many were dropped.
- Exact vs approximate p
- Exact when there are fewer than 50 pairs with no tied or zero differences; otherwise the normal approximation with tie and continuity corrections.
Worked example
The sample has nine people measured under two conditions. The median difference is 0.48 and 8 of the 9 differences are positive:
| Statistic | Value |
|---|---|
| W+ | 40 |
| W− | 5 |
| z | 2.07 |
| p (two-sided, exact) | 0.039 |
| r | 0.69 |
p = 0.039, so the two conditions differ and the first column is higher. Treat the same numbers as two separate groups and the Mann–Whitney test gives p = 0.136: pairing removes person-to-person variation, which makes a change easier to detect.
APA style: W = 5.0, z = 2.07, p = .039, r = .69.
When to use it
- The same subjects measured twice: before and after, left and right eye, two instruments on the same samples.
- The differences are clearly skewed, contain outliers, or are ratings on a short scale.
- If the differences look roughly normal, a paired t-test has more power.
Frequently asked questions
How is it different from the Mann–Whitney U test?
Mann–Whitney compares two separate groups of people. The signed-rank test compares two measurements on the same people, so the rows must be matched.
Can I test one sample against a fixed value?
Yes. Fill the second column with that value. To test whether ratings differ from 3, put 3 in every row of the second column.
Why is the SPSS p-value different?
SPSS shows the asymptotic p without continuity correction by default. Tick "Exact" in SPSS and the results match.
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